US7044691B2 - Forming method for milling threads of variable tooth worms - Google Patents
Forming method for milling threads of variable tooth worms Download PDFInfo
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- US7044691B2 US7044691B2 US10/440,969 US44096903A US7044691B2 US 7044691 B2 US7044691 B2 US 7044691B2 US 44096903 A US44096903 A US 44096903A US 7044691 B2 US7044691 B2 US 7044691B2
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- 238000003801 milling Methods 0.000 title claims abstract description 37
- 238000000034 method Methods 0.000 title claims abstract description 25
- 230000033001 locomotion Effects 0.000 claims abstract description 13
- 230000002596 correlated effect Effects 0.000 claims abstract description 8
- 230000002093 peripheral effect Effects 0.000 claims abstract description 7
- 238000006073 displacement reaction Methods 0.000 claims description 5
- 230000005540 biological transmission Effects 0.000 description 7
- 238000003754 machining Methods 0.000 description 6
- 230000000875 corresponding effect Effects 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
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- 230000004048 modification Effects 0.000 description 1
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F13/00—Making worms by methods essentially requiring the use of machines of the gear-cutting type
- B23F13/02—Making worms of cylindrical shape
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T409/00—Gear cutting, milling, or planing
- Y10T409/10—Gear cutting
- Y10T409/101431—Gear tooth shape generating
- Y10T409/10159—Hobbing
- Y10T409/101749—Process
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T409/00—Gear cutting, milling, or planing
- Y10T409/10—Gear cutting
- Y10T409/101431—Gear tooth shape generating
- Y10T409/10159—Hobbing
- Y10T409/102544—Hobbing including infeed means
- Y10T409/102703—Hobbing including infeed means to infeed along axis of work rotation
- Y10T409/102862—Infeed of cutter
- Y10T409/103021—Infeed of cutter and infeed radially of axis of work rotation
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T409/00—Gear cutting, milling, or planing
- Y10T409/10—Gear cutting
- Y10T409/101431—Gear tooth shape generating
- Y10T409/107473—Making a noncircular gear, worm, rotor, or a planar-faced gear
Definitions
- This invention relates to a forming method for milling the threads of cylindrical variable tooth worms.
- the worm transmissions may be classified into two sorts: the first sort is a cylindrical worm transmission; the second one is a toroidal worm transmission. While the cylindrical worms can further be classified into an involute helicoid worm (ZI for short, the same hereinafter), an Archimedes worm (ZA), a milled helicoid worm (ZK), and a variable tooth worm (VTW) disclosed in China patent No. ZL96244108.2 and U.S. Pat. No. 6,176,148B1 with accordance to the different profile thereof.
- the worms of ZI-, ZA- and ZK-type can all be formed by lathing with different-profile cutters.
- variable tooth worm (VTW) is classified into the cylindrical worms, they cannot be machined on the same facilities with the existing motion relationship even if the cutter were changed seeing that the tooth thickness of the variable tooth worms is changeable along either longitudinal or tooth height direction.
- the minimum tooth thickness of the worms is at the gorge part of the thread, while it gradually thickens toward both ends, as shown in the FIGS. 1 and 2 .
- the worms patented as disclosed in U.S. Pat. No. 1,853,643 with the title of “METHOD OF AND APPARATUS FOR GENERATING THE CONVOLUTE TEETH OR THREADS OF WORMS AND THE LIKE” are machined by using a gear-shape cutter.
- the profile of the cutting edges of the gear shaped cutter for machining the thread of worms in Simmons patent is an involute in the end face.
- the object of the present invention is to supplement the deficiency of the existing technology and to provide a forming method for milling the thread of variable tooth worms with high productivity and high machining accuracy.
- a moving coordinate system ⁇ 1 ( ⁇ 1 )[O 1 ; ⁇ right arrow over (i) ⁇ 1 ( ⁇ 1 ), ⁇ right arrow over (j) ⁇ 1 ( ⁇ 1 ), ⁇ right arrow over (k) ⁇ 1 ( ⁇ 1 )] ⁇ is correlated to the worm blank of variable tooth worms and the worm blank rotates about ⁇ right arrow over (k) ⁇ 1 ( ⁇ 1 )-axis at angular speed ⁇ right arrow over ( ⁇ ) ⁇ 1 ;
- a moving coordinate system ⁇ 2 ( ⁇ 2 )[O 2 ; ⁇ right arrow over (i) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (j) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )] ⁇ is correlated to the milling cutter and the cutter rotates about ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis at angular speed ⁇ right arrow over ( ⁇ )
- the feeding movement of the milling cutter is composed by two components: one component is the radial shift along the ⁇ right arrow over (i) ⁇ 2 (o 2 )-axis; another the peripheral shift around ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis.
- the equations of the cutting edge of the milling cutter are given as below.
- u,v are the parameters of the generatrix plane of variable tooth worm
- ⁇ is the inclination angle of the generatrix plane
- r b is the radius of the main basic circle of the cutter body
- x 2 , y 2 , z 2 are the coordinate values of the generatrix plane.
- the machining method of this invention has higher productivity, more powerful cutting force, less machining hours and reaches higher machining accuracy as compared with other machining method for any cylindrical worm by means of a spatial cutter that has multiple blades thereon, therefore there are multiple edges simultaneously to take part in cutting the VTW worm blank.
- FIGS. 1 and 2 are the schematic views showing the VTW worm and the coordinate system of the prior art of China patent No. ZL96244108.2 (U.S. Pat. No. 6,176,148B1).
- FIG. 3 is a schematic view showing the profile of the cutting edges of the gear shaped cutter of U.S. Pat. No. 1,853,643.
- FIG. 4 is a schematic view showing the relationship between an imaginary cone and a generatrix plane thereof and a coordinate system ⁇ 2 ( ⁇ 2 )[O 2 ; ⁇ right arrow over (i) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (j) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )] ⁇ according the principle of the invention.
- FIG. 5 is a schematic view showing the relationship between disc-shaped cutter and a coordinate system ⁇ 2 ( ⁇ 2 )[O 2 ; ⁇ right arrow over (i) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (j) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (k) ⁇ 2 ( ⁇ 1 )] ⁇ according the principle of the invention.
- FIG. 6 is a schematic view further showing the relationship between disc-shaped cutter and a coordinate system ⁇ 2 ( ⁇ 2 )[O 2 ; ⁇ right arrow over (i) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (j) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )] ⁇ according the principle of the invention.
- FIG. 7 is a schematic view showing forming principle for the method of forming the variable worms according to the invention.
- an imaginary cone with the radius r b of the main basic circle and the half conic angle ⁇ is correlated to the coordinate system ⁇ 2 ( ⁇ 2 )[O 2 ; ⁇ right arrow over (i) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (j) ⁇ 2 ( ⁇ 2 ), ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )] ⁇ , and let a generatrix plane ⁇ be tangential to the cone at point o, the inclination angle of the plane ⁇ relative to k 2 ( ⁇ 2 )-axis be ⁇ , the parameters u and v are introduced to express the characteristics of the plane ⁇ .
- the cutting edge of the disc-shaped cutter is disposed on the generatrix plane ⁇ described by u and v, and is tangential to the circular cone expressed by r b and ⁇ . It is not hard to be seen what the coordinate relationship among the cone and the tangential plan ⁇ as well as a disc-shaped cutter is.
- the generatrix plane ⁇ shall take the cutting edge thereon to rotate about ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis and keeps the tangential state with the cone from beginning to end.
- the cutting edge of the disc-shaped cutter described in this invention is disposed on the generatrix plane ⁇ as shown in the FIG. 6 .
- the milling-cutter rotates around ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis at angular speed
- i 12 and i 12 is a constant;
- the feed motion of the milling cutter comprises the radial shift along ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis and the peripheral shift around ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis.
- u, v are the parameters of the generatrix plane of variable tooth worm
- ⁇ is the inclination angle of the generatrix plane
- r b is the radius of the main basic circle of the cutter body
- x 2 , y 2 , z 2 are the coordinate values of the cutting edge on the generatrix plane.
- FIG. 7 The method of this invention is illustrated in FIG. 7 , showing the relative coordinate relationship between the worm-blank and the milling cutter in the coordinate systems according to the invention.
- Another moving coordinate system ⁇ 1 ( ⁇ 1 )[O 1 ; ⁇ right arrow over (i) ⁇ 1 ( ⁇ 1 ), ⁇ right arrow over (j) ⁇ 1 ( ⁇ 1 ), ⁇ right arrow over (k) ⁇ 1 ( ⁇ 1 )] ⁇ is correlated to the worm blank of the VTW worms, wherein the worm blank of the VTW worms rotates around ⁇ right arrow over (k) ⁇ 1 ( ⁇ 1 )-axis at angular speed
- Embodiment 1 is a diagrammatic representation of Embodiment 1:
- All blades are fully mounted in three dimensions on the milling cutter body and the cutting edges are all located at a spatial generatrix family.
- Embodiment 2 is a diagrammatic representation of Embodiment 1:
- While the milling cutter makes a slight axial displacement with the value ⁇ k 2 1.3 mm along ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis and a differential motion along the tangential direction around ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis besides rotating about ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis at angular speed ⁇ right arrow over ( ⁇ ) ⁇ 2 and simultaneously making a radial feed along ⁇ right arrow over (i) ⁇ 2 (o 2 )-axis and a peripheral feed around ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis.
- the feed motion of the milling cutter is combined by three componential motions: the shift of the milling cutter along ⁇ right arrow over (i) ⁇ 2 (o 2 )-axis, the shift thereof along ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis and the tangential shift thereof while rotating around ⁇ right arrow over (k) ⁇ 2 ( ⁇ 2 )-axis.
- the milling cutter will completely envelop the thread of the VTW worms.
- All blades are fully mounted in three dimensions on the milling cutter body and the cutting edges are all located at a spatial generatrix family.
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Gears, Cams (AREA)
- Milling Processes (AREA)
Abstract
A forming method for milling teeth of variable tooth worms (VTW) with the following features: on a multi-axis simultaneously-working CNC machine-tool a moving coordinate system {σ1(φ1)[O1;{right arrow over (i)}1(φ1),{right arrow over (j)}1(φ1),{right arrow over (k)}1 (φ1)]} is correlated to the worm blank of the VTW worms, whereon the worm blank of the VTW worms rotates around {right arrow over (k)}1(φ1)-axis at angular speed |{right arrow over (ω)}1|; another moving coordinate system {σ2(φ2)[O2; {right arrow over (i)}2(φ2), {right arrow over (j)}2(φ2), {right arrow over (k)}2(φ2)]} is correlated to the milling cutter, whereon the milling-cutter rotates around {right arrow over (k)}2(φ2)-axis at angular speed |{right arrow over (ω)}2|, |{right arrow over (ω)}1|/|{right arrow over (ω)}2|=i12 and i12 is a constant; the feed motion of the milling cutter comprises the radial shift along {right arrow over (i)}2(o2)-axis and the peripheral shift around {right arrow over (k)}2(φ2)-axis; the equations of the cutting edge of the milling cutter are given as below
x=u
y 2 =r b −v sin β
z 2 =v cos β.
x=u
y 2 =r b −v sin β
z 2 =v cos β.
Description
This application is a continuation-in-part application of application Ser. No. 09/978,340 now abandoned, filed Oct. 17, 2001, entitled “METHOD OF FORMING MILLED TOOTH OF VARIABLE TOOTH WORM”.
This invention relates to a forming method for milling the threads of cylindrical variable tooth worms.
The worm transmissions may be classified into two sorts: the first sort is a cylindrical worm transmission; the second one is a toroidal worm transmission. While the cylindrical worms can further be classified into an involute helicoid worm (ZI for short, the same hereinafter), an Archimedes worm (ZA), a milled helicoid worm (ZK), and a variable tooth worm (VTW) disclosed in China patent No. ZL96244108.2 and U.S. Pat. No. 6,176,148B1 with accordance to the different profile thereof. The worms of ZI-, ZA- and ZK-type can all be formed by lathing with different-profile cutters. However, the relationship of the relative movement between the workpiece and the cutter is the same. Alternatively, the different types of worms such as ZI, ZA and ZK can be machined on the same machine tool with the worm blank turning and the cutter feeding along the longitudinal and radial directions relatively to the worm blank, the one thing must be done only is to change the corresponding cutter. Although the variable tooth worm (VTW) is classified into the cylindrical worms, they cannot be machined on the same facilities with the existing motion relationship even if the cutter were changed seeing that the tooth thickness of the variable tooth worms is changeable along either longitudinal or tooth height direction. The minimum tooth thickness of the worms is at the gorge part of the thread, while it gradually thickens toward both ends, as shown in the FIGS. 1 and 2 .
The worms patented as disclosed in U.S. Pat. No. 1,853,643 with the title of “METHOD OF AND APPARATUS FOR GENERATING THE CONVOLUTE TEETH OR THREADS OF WORMS AND THE LIKE” (hereinafter referred to as Simmons patent) are machined by using a gear-shape cutter. The profile of the cutting edges of the gear shaped cutter for machining the thread of worms in Simmons patent is an involute in the end face. Let the radius of the basic cylindroid of the gear shaped cutter be rb, the intersected line of tangential plane Σ with the side surface of the cutter tooth is a straight line as shown in the FIG. 3 . Therefore, Simmons method for forming the involute worms can not be used for forming the thread of variable tooth worms with a circular toroid, or an elliptic toroid, or a parabolic toroid.
The object of the present invention is to supplement the deficiency of the existing technology and to provide a forming method for milling the thread of variable tooth worms with high productivity and high machining accuracy.
In order to realize the object, the following technical solution will be adopted. A moving coordinate system {σ1(φ1)[O1; {right arrow over (i)}1 (φ1), {right arrow over (j)}1 (φ1), {right arrow over (k)}1(φ1)]} is correlated to the worm blank of variable tooth worms and the worm blank rotates about {right arrow over (k)}1(φ1)-axis at angular speed {right arrow over (ω)}1; A moving coordinate system {σ2(φ2)[O2; {right arrow over (i)}2 (φ2), {right arrow over (j)}2(φ2), {right arrow over (k)}2(φ2)]} is correlated to the milling cutter and the cutter rotates about {right arrow over (k)}2(φ2)-axis at angular speed {right arrow over (ω)}2, whereof |{right arrow over (ω)}1|/|{right arrow over (ω)}2|=i12, i12 is a constant. The feeding movement of the milling cutter is composed by two components: one component is the radial shift along the {right arrow over (i)}2(o2)-axis; another the peripheral shift around {right arrow over (k)}2(φ2)-axis. The equations of the cutting edge of the milling cutter are given as below.
x=u
y 2 =r b −v sin β
z 2 =v cos β
Where, u,v are the parameters of the generatrix plane of variable tooth worm; β is the inclination angle of the generatrix plane; rb is the radius of the main basic circle of the cutter body; x2, y2, z2 are the coordinate values of the generatrix plane.
x=u
y 2 =r b −v sin β
z 2 =v cos β
Where, u,v are the parameters of the generatrix plane of variable tooth worm; β is the inclination angle of the generatrix plane; rb is the radius of the main basic circle of the cutter body; x2, y2, z2 are the coordinate values of the generatrix plane.
The advantages and the effect of this invention show that the machining method of this invention has higher productivity, more powerful cutting force, less machining hours and reaches higher machining accuracy as compared with other machining method for any cylindrical worm by means of a spatial cutter that has multiple blades thereon, therefore there are multiple edges simultaneously to take part in cutting the VTW worm blank.
By referring to the attached drawings and embodiments, the technical scheme of the invention is further expounded as follows:
As shown in the FIGS. 4 and 7 , an imaginary cone with the radius rb of the main basic circle and the half conic angle β is correlated to the coordinate system {σ2(φ2)[O2; {right arrow over (i)}2 (φ2), {right arrow over (j)}2 (φ2), {right arrow over (k)}2(φ2)]}, and let a generatrix plane Σ be tangential to the cone at point o, the inclination angle of the plane Σ relative to k2(φ2)-axis be β, the parameters u and v are introduced to express the characteristics of the plane Σ. In this invention the cutting edge of the disc-shaped cutter is disposed on the generatrix plane Σ described by u and v, and is tangential to the circular cone expressed by rb and β. It is not hard to be seen what the coordinate relationship among the cone and the tangential plan Σ as well as a disc-shaped cutter is. The relationship between disc-shaped cutter and the coordinate system {σ2(φ2)[O2; {right arrow over (i)}2 (φ2), {right arrow over (j)}2 (φ2), {right arrow over (k)}2(φ2)]}, will be further described, as jointly viewed with FIGS. 5 and 6 .
As shown in the FIGS. 5 and 6 , while the described disc-shaped cutter rotates about its own {right arrow over (k)}2(φ2)-axis, the generatrix plane Σ shall take the cutting edge thereon to rotate about {right arrow over (k)}2(φ2)-axis and keeps the tangential state with the cone from beginning to end. The cutting edge of the disc-shaped cutter described in this invention is disposed on the generatrix plane Σ as shown in the FIG. 6 . When the generatrix plane Σ tangential to the cone rotates about {right arrow over (k)}2(φ2)-axis up to a position I, a row of the cutting edges are distributed on the generatrix plane Σ with the inclination angle β, while the generatrix plane Σ tangential to the cone rotates about {right arrow over (k)}2(φ2)-axis up to another position II, another row of the cutting edges are also on the generatrix plane Σ, the inclination angle of the generatrix plane Σ is still β. The milling-cutter rotates around {right arrow over (k)}2(φ2)-axis at angular speed |{right arrow over (ω)}2|, |{right arrow over (ω)}1|/|{right arrow over (ω)}2|=i12 and i12 is a constant; the feed motion of the milling cutter comprises the radial shift along {right arrow over (k)}2(φ2)-axis and the peripheral shift around {right arrow over (k)}2(φ2)-axis. The coordinate values of any point on the cutting edge are all calculated according to the equations disclosed as follows:
x=u
y 2 =r b −v sin β
z 2 =v cos β
Where, u, v are the parameters of the generatrix plane of variable tooth worm; β is the inclination angle of the generatrix plane; rb is the radius of the main basic circle of the cutter body; x2, y2, z2 are the coordinate values of the cutting edge on the generatrix plane.
x=u
y 2 =r b −v sin β
z 2 =v cos β
Where, u, v are the parameters of the generatrix plane of variable tooth worm; β is the inclination angle of the generatrix plane; rb is the radius of the main basic circle of the cutter body; x2, y2, z2 are the coordinate values of the cutting edge on the generatrix plane.
The method of this invention is illustrated in FIG. 7 , showing the relative coordinate relationship between the worm-blank and the milling cutter in the coordinate systems according to the invention. Another moving coordinate system {σ1(φ1)[O1; {right arrow over (i)}1 (φ1), {right arrow over (j)}1 (φ1), {right arrow over (k)}1(φ1)]} is correlated to the worm blank of the VTW worms, wherein the worm blank of the VTW worms rotates around {right arrow over (k)}1(φ1)-axis at angular speed |{right arrow over (ω)}1|, therefore shifting of cutting edge of the cutter on the cutter head according to the method of the invention on the inclined generatrix plane in spatial locations is to envelop out and form the tooth flank of variable worms in the worm blank.
The detailed explanations of the method of this invention are given by following preferred embodiments.
Embodiment 1:
On a five-simultaneously-working-axis CNC machine-tool, given that a VTW worm to be machined has β=18° the inclination angle of the generatrix plane, d1=50.2 mm the reference diameter, and the center distance between the worm blank and the milling-cutter a=101.6 mm, the milling-cutter performs a cutting movement relatively to the worm blank with the transmission ratio between the worm blank and the milling cutter i=41/4; the worm blank rotates around {right arrow over (k)}1(φ1)-axis at angular speed {right arrow over (ω)}1, while the milling cutter rotates about {right arrow over (k)}2(φ2)-axis at angular speed {right arrow over (ω)}2 and simultaneously makes a radial feed along {right arrow over (i)}2(o2)-axis and a peripheral feed around {right arrow over (k)}2(φ2)-axis. The radius of the main basic circle of the milling cutter rb=33 mm and the coordinate values of the cutting edge of the milling cutter are described according to the following equations
x2=u,
y 2 =r b −v sin β,
z 2 =v cos β.
Where,
x2=u,
y 2 =r b −v sin β,
z 2 =v cos β.
Where,
-
- u=64˜74
- v=−24˜24
- when u=70, v=−12, then
- x2=70 mm,
- y2=33−(−12×sin 18°)=36.708 mm,
- z2=−12×cos 18°=−11.413 mm.
All blades are fully mounted in three dimensions on the milling cutter body and the cutting edges are all located at a spatial generatrix family.
Embodiment 2:
On a five-simultaneously-working-axis CNC machine-tool, given that a VTW worm to be machined has β=18° the inclination angle of the generatrix plane, d1=50.2 mm the reference diameter, and the center distance between the worm blank and the milling-cutter a=101.6 mm, the milling-cutter performs a cutting movement relatively to the worm blank with the transmission ratio between the worm blank and the milling cutter i=41/4.
Besides rotating around {right arrow over (k)}1(φ1)-axis at angular speed {right arrow over (ω)}1, the worm blank also makes a slight axial displacement along {right arrow over (k)}1(φ1)-axis with the value Δk1=1.05 mm in order to make the reference toroid of VTW worm become an elliptic or parabolic one.
While the milling cutter rotates about {right arrow over (k)}2(φ2)-axis at angular speed {right arrow over (ω)}2 and simultaneously makes a radial feed along {right arrow over (i)}2(o2)-axis and a peripheral feed around {right arrow over (k)}2(φ2)-axis.
The radius of the main basic circle of the milling cutter rb=33 mm and the coordinate values of the cutting edge of the milling cutter are described according to the following equations
x2=u,
y 2 =r b −v sin β
z 2 =v cos β.
Where,
x2=u,
y 2 =r b −v sin β
z 2 =v cos β.
Where,
-
- u=64˜74
- v=−24˜24
- when u=70, v=−12, then
- x2=70 mm,
- y2=33−(−12×sin 18°)=36.708 mm,
- z2=−12×cos 18°=−11.413 mm.
All blades are fully mounted in three dimensions on the milling cutter body and the cutting edges are all located at a spatial generatrix family.
Embodiment 3:
On a five-simultaneously-working-axis CNC machine-tool, given that a VTW worm to be machined has β=15.9° the inclination angle of the generatrix plane, d1=50 mm the reference diameter, and the center distance between the worm blank and the milling-cutter a=125 mm, the milling-cutter performs a cutting movement relatively to the worm blank with the transmission ratio between the worm blank and the milling cutter i=42/3.
Besides rotating around {right arrow over (k)}1(φ1)-axis at angular speed {right arrow over (ω)}1, the worm blank also makes a slight axial displacement along {right arrow over (k)}1(φ1)-axis with the value Δk1=1.1 mm in order to make the reference toroid of VTW worm become an elliptic or parabolic one.
While the milling cutter makes a slight axial displacement with the value Δk2=1.3 mm along {right arrow over (k)}2(φ2)-axis and a differential motion along the tangential direction around {right arrow over (k)}2(φ2)-axis besides rotating about {right arrow over (k)}2(φ2)-axis at angular speed {right arrow over (ω)}2 and simultaneously making a radial feed along {right arrow over (i)}2(o2)-axis and a peripheral feed around {right arrow over (k)}2(φ2)-axis. Alternatively, the feed motion of the milling cutter is combined by three componential motions: the shift of the milling cutter along {right arrow over (i)}2(o2)-axis, the shift thereof along {right arrow over (k)}2(φ2)-axis and the tangential shift thereof while rotating around {right arrow over (k)}2(φ2)-axis. In this case the milling cutter will completely envelop the thread of the VTW worms.
The radius of the main basic circle of the milling cutter rb=38 mm and the coordinate values of the cutting edge of the milling cutter are described according to the following equations:
x2=u,
y 2 =r b −v sin β
z 2 =v cos β.
Where,
x2=u,
y 2 =r b −v sin β
z 2 =v cos β.
Where,
-
- u=80˜93
- v=−30˜30
- when u=90, v=15, then
- x2=90 mm,
- y2=38−15×sin 15.9°=33.891 mm,
- z2=15×cos 15.9°=14.426 mm.
All blades are fully mounted in three dimensions on the milling cutter body and the cutting edges are all located at a spatial generatrix family.
Other preferred embodiments can be given on the basis of following parameters: assuming that the range of the center distance a of such worm transmissions is from 80 mm to 500 mm, the values of u, v and rb can be recommended as listed in the following table.
| TABLE 1 | |||||||||
| Center distance α | |||||||||
| (Unit: mm) | 80 | 100 | 125 | 160 | 200 | 250 | 315 | 400 | 500 |
| μ | 51~68 | 64~74 | 80~93 | 102~119 | 128~149 | 163~189 | 205~238 | 261~303 | 326~378 |
| ν | ±19.4 | ±24.3 | ±30.4 | ±38.9 | ±48.6 | ±60.7 | ±76.5 | ±97.2 | ±122 |
| rb(Unit: mm) | 19~28 | 24~35 | 30~43 | 39~56 | 48~69 | 61~67 | 76~109 | 97~138 | 122~173 |
| Remark: 0° ≦ β ≦ 30° |
Although preferred embodiments of the invention have been described above, this invention is not limited to the particular structures and features described in detail herein. It will be apparent to those skilled in the art that numerous modifications form part of the invention insofar as they do not depart from the scope of the appended claims.
Claims (12)
1. A forming method for milling teeth of variable tooth worms, comprising the following steps:
on a multi-axis simultaneously-working CNC machine-tool, a first moving coordinate system {σ1(φ1)[O1; i1(φ1); j1(φ1), k1(φ1)]} is correlated to the worm blank of the VTW worms, wherein the worm blank of the VTW worms rotates around k1(φ1)-axis at angular speed |ω1|; a second moving coordinate system {σ2(φ2)[O2; i2(φ2); j2(φ2), k2(φ2)]} is correlated to the milling cutter, wherein the milling-cutter rotates around k2(φ2)-axis at angular speed |ω2|, |ω1|/|ω2|=i12 and i12 is a constant; the feed motion of the milling cutter comprises the radial shift along the i2(O2)-axis and the peripheral shift around the k2(φ2)-axis; the equations of each cutting edge of the milling cutter are given as follows:
x2=u
y 2 =r b −v sin β
z 2 =v cos β
x2=u
y 2 =r b −v sin β
z 2 =v cos β
where, u, v are the parameters of a generatrix plane Σ of the variable tooth worms tangent to an imaginary cone; β is the inclination angle of the generatrix plane Σ relative to the axis of the imaginary cone; rb is the radius of the main basic circle of the cutter body; x2, y2, z2 are the coordinate values of the cutting edge on the generatrix plane, in which when the center distance between the worm blank and the milling-cutter is from 80 mm to 500 mm, the value of u is from 51 to 378, the value of v is from ±19.4 to ±122, and the value of rb is from 19 mm to 173 mm; and βis greater than 0° and less than or equal to 30°;
and shifting of a cutting edge of the cutter on the inclined generatrix plane in spatial locations about the milling cutter forms a cutter that will form the tooth flank of the variable tooth worms in the worm blank.
2. The method as described in the claim 1 , wherein the worm blank makes a slight axial displacement along {right arrow over (k)}1(φ1)-axis.
3. The method as described in the claim 1 or claim 2 , wherein the milling cutter makes both a slight displacement along axis {right arrow over (k)}2(φ2)-axis and a differential feeding motion along the tangential direction around {right arrow over (k)}2(φ2)-axis.
4. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling cutter is 80 mm, the value of u is from 51 to 68, the value of v is ±19.4, and the value of rb is from 19 mm to 28 mm.
5. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 100 mm, the value of u is from 64 to 74, the value of v is ±24.3, and the value of rb is from 24 mm to 35 mm.
6. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 125 mm, the value of u is from 80 to 93, the value of v is ±30.4, and the value of rb is from 30 mm to 43 mm.
7. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 160 mm, the value of u is from 102 to 118, the value of v is ±38.9, and the value of rb is from 39 mm to 56 mm.
8. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 200 mm, the value of u is from 128 to 149, the value of v is ±48.6, and the value of rb is from 48 mm to 69 mm.
9. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 250 mm, the value of u is from 163 to 189, the value of v is ±60.7, and the value of rb is from 61 mm to 87 mm.
10. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 315 mm, the value of u is from 205 to 238, the value of v is ±76.5, and the value of rb is from 76 mm to 109 mm.
11. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 400 mm, the value of u is from 261 to 303, the value of v is ±97.2, and the value of rb is from 97 mm to 138 mm.
12. The method as described in the claim 1 , wherein when center distance between the worm blank and the milling-cutter is 500 mm, the value of u is from 326 to 378, the value of v is ±122, and the value of rb is from 122 mm to 173 mm.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US10/440,969 US7044691B2 (en) | 2000-12-01 | 2003-05-19 | Forming method for milling threads of variable tooth worms |
Applications Claiming Priority (4)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN00133681.9 | 2000-12-01 | ||
| CNB001336819A CN1137795C (en) | 2000-12-01 | 2000-12-01 | Method for milling teeth of tooth-variable worm |
| US09/978,340 US20020067966A1 (en) | 2000-12-01 | 2001-10-17 | Method of forming milled tooth of variable tooth worm |
| US10/440,969 US7044691B2 (en) | 2000-12-01 | 2003-05-19 | Forming method for milling threads of variable tooth worms |
Related Parent Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| US09/978,340 Continuation-In-Part US20020067966A1 (en) | 2000-12-01 | 2001-10-17 | Method of forming milled tooth of variable tooth worm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| US20040033114A1 US20040033114A1 (en) | 2004-02-19 |
| US7044691B2 true US7044691B2 (en) | 2006-05-16 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| US10/440,969 Expired - Lifetime US7044691B2 (en) | 2000-12-01 | 2003-05-19 | Forming method for milling threads of variable tooth worms |
Country Status (1)
| Country | Link |
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| US (1) | US7044691B2 (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050272354A1 (en) * | 2004-06-08 | 2005-12-08 | Koji Kidowaki | Method and apparatus for manufacturing hourglass worm rolling die |
| US20160201759A1 (en) * | 2013-08-14 | 2016-07-14 | Sew-Eurodrive Gmbh & Co. Kg | Gearing having a pinion and a wheel |
| WO2019190972A1 (en) * | 2018-03-27 | 2019-10-03 | Kinematics, Llc | Tooth gap relieved enveloping worm |
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|---|---|---|---|---|
| US20050272354A1 (en) * | 2004-06-08 | 2005-12-08 | Koji Kidowaki | Method and apparatus for manufacturing hourglass worm rolling die |
| US7169023B2 (en) * | 2004-06-08 | 2007-01-30 | Asmo Co., Ltd. | Method and apparatus for manufacturing hourglass worm rolling die |
| US20160201759A1 (en) * | 2013-08-14 | 2016-07-14 | Sew-Eurodrive Gmbh & Co. Kg | Gearing having a pinion and a wheel |
| US9964180B2 (en) * | 2013-08-14 | 2018-05-08 | Sew-Eurodrive Gmbh & Co. Kg | Gearing having a pinion and a wheel |
| WO2019190972A1 (en) * | 2018-03-27 | 2019-10-03 | Kinematics, Llc | Tooth gap relieved enveloping worm |
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|---|---|
| US20040033114A1 (en) | 2004-02-19 |
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